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Ta có: \(\frac{x-y}{3}=\frac{x+y}{13}=\frac{x-y+x+y}{16}=\frac{2x}{16}=\frac{x}{8}=\frac{25x}{200}=\frac{xy}{200}\)
Suy ra: \(25x=xy\Rightarrow y=25\)
Ta có: \(\frac{x-y}{3}=\frac{x+y}{13}\)
Suy ra: \(13x-13y=3x+3y\)
Thế y vào đẳng thức trên:
\(13x-325=3x+75\)
Suy ra: \(10x=325+75=400\Rightarrow x=40\)
Vậy ........
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Xét tam giác ABC có A = 180 - C - B =180 - 120 - 30 = 30
Vì AE là phân giác góc ngoài tại A
=> BAE = ( 180 - A ) / 2 = ( 180 - 30 ) / 2 = 75
Có ABE + ABC = 180
=> ABE = 180 - ABC = 180 - 120 = 60
Xét tam giác AEB có BEA + BAE + ABE = 180
=> AEB = 180 - 60 -75 = 45
Vậy AEB = 45
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\(M=2021+\left(x-2022\right)^{2022}\ge2021\forall x\)
Dấu '=' xảy ra khi x=2022
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\(B=|2014-2x|+|2016-2x|\)
\(=|2014-2x|+|2x-2016|\ge|2014-2x+2x-2016|\)
Hay \(B\ge2\)
Dấu"="xảy ra \(\Leftrightarrow\left(2014-2x\right)\left(2x-2016\right)\ge0\)
\(\Leftrightarrow\hept{\begin{cases}2014-2x\ge0\\2x-2016\ge0\end{cases}}\)hoặc \(\hept{\begin{cases}2014-2x< 0\\2x-2016< 0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2x\le2014\\2x\ge2016\end{cases}\left(loai\right)}\)hoặc\(\hept{\begin{cases}2x>2014\\2x< 2016\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x>1007\\x< 1008\end{cases}}\)
\(\Leftrightarrow1007< x< 1008\)
Vậy \(B_{min}=2\)\(\Leftrightarrow1007< x< 1008\)